Colloquium

When a large number of quantum mechanical particles are put together and allowed to interact, various condensed matter phases emerge with macroscopic quantum properties. While conventional quantum phases like superfluids or quantum magnets can be understood as a simple collection of
single particle quantum states, recent discoveries of fractional quantum Hall or spin liquids states contain intrinsic entanglement among all the particles. To understand such unconventional phases requires unconventional methods. In this talk, I will discuss how the quantum information insights about many-body entanglement gives us a unique perspective and a powerful tool to study these
unconventional phases. In particular, starting from simple entanglement building blocks, we are able to construct new gapped quantum phases, classify all possible gapped phases in certain cases and obtain a better understanding of the structure of the phase diagram. With these progress, we expect the many-body entanglement point of view to play an important role in our effort to map the full quantum phase diagram, leading to breakthroughs in our understanding of gapless phases and phase transitions and in the development of numerical tools to simulate such systems.

Shor's algorithm can be a meaningful test for experimental quantum processing systems, when suitably realized.  I present results from a  recent implemenation of quantum factoring using trapped ion qubits, demonstrating feed-forward control, use of quantum memory during computation, and cascaded three-qubit gates.  Such capabilities are necessary ingredients for a future large-scale,
fault-tolerant quantum computing system.

The direct detection of gravitational waves promises to open up a new spectrum that is otherwise mostly closed to electromagnetically based astronomical observations. Detecting gravitational waves from binary black holes and neutron stars, as well as estimating their parameters, requires a sufficiently accurate prediction for the expected waveform signal. Unfortunately, the state of the art for the pillars of gravitational wave theory -- numerical relativity, the post-Newtonian approximation, and linear black hole perturbation theory -- have yet to cover accurately the entire parameter space even when taken together. In this talk, I present a new direction for systematically describing compact binaries that is valid over a potentially very large portion of the parameter space.

The approach uses high-order black hole perturbation theory in the mass ratio together with ideas and techniques borrowed from effective field theory for incorporating the physics of extended masses like spin and tidal effects. I discuss recent advances, future prospects, and potential impacts in this direction.

While quantum measurement remains the central philosophical conundrum of quantum mechanics, it has recently grown into a respectable (read: experimental!) discipline as well.  New perspectives on measurement have grown  out of new technological possibilities, but also out of
attempts to design systems for quantum information processing, which promise to be exponentially more powerful than any possible classical computer.  I will try to give a flavour about some of these perspectives, focussing largely on a particular paradigm known as "weak measurement."
Weak measurement is a natural extension of a pragmatic view of what it means to measure something about a quantum system, yet leads to some rather surprising results.  I will describe a few examples of our recent experiments using weak measurement to probe fundamental issues in  uantum mechanics such as what the minimum disturbance due to a quantum measurement is.  I will also argue that there are regimes in which weak measurement offers a practical advantage for sensitive measurements.  

The ground-based gravitational-wave telescopes LIGO and Virgo approach the era of first detections.  Gravitational-wave observations will provide a unique probe for exploring strong-field general relativity and compact-binary astrophysics.  In this talk, I describe recent predictions regarding the distributions of black-hole and neutron-star binary mergers, and progress on solving the inverse problem of turning gravitational-wave observations into astrophysical information. I highlight some exciting recent investigations into the use of gravitational waves as tests of general relativity.

Causal set quantum gravity is based on the marriage between the concept of causality as an organising principle more basic even than space or time and fundamental atomicity. Causal sets suggest novel possibilities for "dynamical laws" in which spacetime grows by the accumulation of new spacetime atoms, potentially realising within physics C.D. Broad's concept of a growing block universe
in which the past is real and the future is not. To do justice to relativity and general covariance, the atoms must accumulate in a partial order, exactly the order that the atoms have physically amongst themselves. That this is possible is demonstrated by the Rideout-Sorkin Classical Stochastic Growth models. This proof of concept -- of the compatibility of relativity and ``becoming'' -- is, however, classical and is challenged by the global character of the physical world within a path integral framework for quantum theory. Out of the struggle to reconcile the global and local natures of the physical world may arise a quantal dynamics for causal sets.

One of the main challenges that we face both as individual persons and as a species concerns the distribution and use of resources, such as water, time, capital, computing power or negatively valued
resources like nuclear waste. Also within theoretical physics, one frequently deals with resources like free energy or quantum entanglement. I will describe a mathematical theory of resources which makes quantitative predictions about how many resources are required for producing a certain commodity and outline some applications to information theory.
Joint work with Bob Coecke and Rob Spekkens.